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We consider the design of capacity-approaching forward error correction (FEC) systems for use in the aeronautical telemetry environment. The modulation format is the bandwidth-efficient telemetry-group version of shaped-offset quadrature phase-shift keying (SOQPSK-TG). The FEC codes are a low-density parity-check (LDPC) code and a serially concatenated convolutional code (SCCC). The block structure of the two types of FEC is designed such that the two code words are formatted as similarly as possible. This unified format allows the flexibility of the FEC-encoded signal to be received by legacy test-range assets that are not equipped with FEC¿although no coding gain is realized in such a case. We also show how a wide range of near-optimal SOQPSK demodulators can be paired with the FEC decoders; this includes the most widely deployed SOQPSK demodulator (the so-called symbol-by-symbol (SxS) demodulator), which so far has not been considered for use in FEC applications. In all of our demodulator/decoder designs, we apply techniques that are simple and robust and that fully decouple the demodulator's tasks (e.g., synchronization, filtering) from the decoder's tasks (e.g., path metrics, soft outputs). For both LDPC and SCCC, we show that very attractive system designs can perform within 0.5 dB of optimum, while requiring only a fraction of the complexity of the optimum system.